$$\displaystyle\frac{d}{d x } \left( \frac{ \sqrt{ 1- \cos x } }{ 2 } \right)$$
$\frac{\sin(x)}{4\sqrt{-\cos(x)+1}}$
$\frac{2\cos(x)\left(-\cos(x)+1\right)-\left(\sin(x)\right)^{2}}{8\left(-\cos(x)+1\right)^{\frac{3}{2}}}$
